On which curve does the perpendicular tangents drawn to the hyperbola `(x^(2))/(25)-(y^(2))/(16)=1` intersect?
Text Solution
AI Generated Solution
To solve the problem of determining the curve on which the perpendicular tangents drawn to the hyperbola \(\frac{x^2}{25} - \frac{y^2}{16} = 1\) intersect, we can follow these steps:
### Step 1: Identify the hyperbola parameters
The given hyperbola is in the standard form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), where:
- \(a^2 = 25\) (thus \(a = 5\))
- \(b^2 = 16\) (thus \(b = 4\))
### Step 2: Determine the equation of the director circle
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